Preheat the oven to 220C/425F/Gas 7.
For the herb crust, place all of the crust ingredients into a food processor and pulse briefly to combine.
For the lamb, heat some oil in a frying pan until nearly smoking.
Season the lamb racks well with salt and freshly ground black pepper, then fry, turning occasionally, until crisp and brown on all sides.
Remove from the pan and brush the rounded, flesh-side of each rack with the mustard.
Press the herb crust mixture onto the layer of mustard on each rack.
Place the lamb racks into a large roasting tin and transfer to the oven to roast for 20-25 minutes, or until cooked to your liking.
Meanwhile, for the bean gratin, heat the olive oil in a frying pan over a medium heat.
Add the shallots, celery, garlic and carrot and fry until softened.
Remove the pan from the heat, add the beans and crème fraîche and stir in gently.
Season the bean mixture with salt and freshly ground black pepper and transfer to a shallow ovenproof dish.
Place the breadcrumbs, parmesan and butter into a bowl and mix well. Sprinkle the breadcrumb mixture over the bean mixture.
Remove the lamb from the oven. Set aside, cover loosely with kitchen foil and allow to rest for 20 minutes.
Reduce the oven temperature to 200C/400F/Gas 6.
Place the bean gratin into the oven to bake for 20 minutes, or until golden and crisp on top.
To serve, carve the lamb and place onto plates with a spoonful of bean gratin alongside.